Schwinger's picture of quantum mechanics: 2-groupoids and symmetries
- URL: http://arxiv.org/abs/2104.13880v1
- Date: Wed, 28 Apr 2021 16:53:56 GMT
- Title: Schwinger's picture of quantum mechanics: 2-groupoids and symmetries
- Authors: Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo and
Luca Schiavone
- Abstract summary: It is shown that, given a groupoid $Grightarrows Omega$ associated with a (quantum) system, there are two possible descriptions of its symmetries.
On the other hand, taking advantage of the notion of group of bisections of a given groupoid, the global perspective allows to construct a group of symmetries out of a 2-groupoid.
The latter notion allows to introduce an analog of the Wigner's theorem for quantum symmetries in the groupoid approach to Quantum Mechanics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Starting from the groupoid approach to Schwinger's picture of Quantum
Mechanics, a proposal for the description of symmetries in this framework is
advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$
associated with a (quantum) system, there are two possible descriptions of its
symmetries, one "microscopic", the other one "global".The microscopic point of
view leads to the introduction of an additional layer over the grupoid $G$,
giving rise to a suitable algebraic structure of 2-groupoid.On the other hand,
taking advantage of the notion of group of bisections of a given groupoid, the
global perspective allows to construct a group of symmetries out of a
2-groupoid.The latter notion allows to introduce an analog of the Wigner's
theorem for quantum symmetries in the groupoid approach to Quantum Mechanics.
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